There can be no greater boost for a struggling indie band than having the biggest rock star in the world cover one of your songs as part of a landmark TV performance. Unfortunately, by the time Kurt Cobain croaked his way through Jesus Doesn't Want Me for a Sunbeam during Nirvana's 1993 MTV Unplugged set, its writers – Glasgow lo-fi legends the Vaselines – had already called it quits.

Formed in 1986 by then-couple Eugene Kelly and Frances McKee, the Vaselines recorded only 19 songs together before disillusionment set in. However, thanks in part to Cobain's patronage – Nirvana's Incesticide compilation contained covers of two more Vaselines numbers, Molly's Lips and Son of a Gun – their sweetly insouciant brand of scruffy garage pop won plenty of posthumous fans when Sub Pop reissued their catalogue in 1992.

Persuaded to re-form for a charity gig in 2008, McKee and Kelly were astonished to come across a whole new generation of bands – Vivian Girls, the Pains of Being Pure at Heart, Dum Dum Girls and more – fashioned in their image. It was sufficient encouragement for the pair to complete their long-awaited second album, set for release this September on Sub Pop. Saucily entitled Sex With an X, its 12 slapdash singalongs display a charming disdain for boring concepts like development and maturity.

How does it feel to have a new Vaselines album to promote more than 20 years after you split up?

Eugene: It feels pretty good. Like everything the Vaselines have ever done, it's been completely unplanned. The whole reunion happened by chance – we got back together for a charity show, then we took up some offers to play in America. We wrote some new songs to fill out the set, and suddenly we had an album's worth. The band's been back together for two years now, and it's still fun.

Frances: It's nice to get a second chance, because I've sometimes felt in the past that the Vaselines were a joke that people didn't really get.

In the process of making this new record, have you become more aware of the qualities that define the Vaselines?

F: Yes. The main thrust of the Vaselines is that Eugene and I sing together, and that our voices complement each other. And I've learned that, 20 years on, we still can't play too well! That shines through quite clearly. We're still not very professional.

E: We record quickly and don't work things to death, which I think keeps the excitement up.

F: Also both Eugene and I have a very stupid, childlike sense of humour and that's remained with us – for example, calling our album Sex With an X. I did have to go to my husband and check he was OK with that!

Presumably there was a period after your romance failed when you couldn't stand the sight of each other, so how did you get to the point where you wanted to work together again?

F: I think inevitably when couples split up there's always that period of disharmony – although I was blameless of course!

E: But we were friends again within 18 months. We even got the Vaselines back together for a one-off gig to support Nirvana in Edinburgh in 1991. So when it came to reforming the band for good, it wasn't like we needed an intermediary to get us chatting. Now we find it very easy to write. You'd think that maybe after 20 years we wouldn't be so simpatico, but because there are parameters to what a Vaselines song can say, it was easy enough to go, "Let's just write a song like the Vaselines".

Has it been strange to find yourself playing on festival bills with young bands that owe an obvious debt to the Vaselines?

F: Until we went to America for the first time [in 2008], I didn't realise how important the Vaselines were to some people over there. I met up with Dum Dum Girls [who are named after a Vaselines lyric] when they played in Glasgow. It's a complete compliment for a band to say they've been inspired by what you've done, especially when they've come up with something so brilliant themselves.

E: It's weird, because before we were the snotty kids on the bill and now we're the adults!

Who were your role models when you were starting out?

E: Obviously the Velvet Underground. Nancy Sinatra and Lee Hazlewood were a big influence because we knew we wanted to sing duets. And Pussy Galore and Sonic Youth – even though we couldn't play like them, we wanted to get some of their raw energy into what we were doing.

F: Bands like the Television Personalities, Orange Juice, the Pastels, the Jesus and Mary Chain. Bands who made you realise that anyone could do it – you didn't even have to be particularly talented, you just had to have bit of guts. I only learned to play the guitar so I could be in a band. I don't even think I could play five chords at the time, so what people call the naivety of the Vaselines was just pandering to my incompetence.

Why did you get disillusioned with the Vaselines so rapidly first time around?

F: It was a whole lot of things. Every venue we played in was always freezing, we were always starving. And of course we had no money. Everything just seemed quite grim after a while. Also it was a huge disappointment when our album was shelved – it was going to come out on 53rd & 3rd but they went bust. At the time we thought nobody would ever get to hear it. Rough Trade eventually picked it up, but by that time we'd split up.

E: We thought there was no future for us. There was no buzz about us, we didn't have a label, we didn't have any sort of management. I thought, "We've done what we can with this, it's probably time to do something different."

So was it bittersweet to receive all that attention via Nirvana after you'd split?

E: Not bittersweet, just sweet. Any sort of recognition for what you've done is good. We never regretted not having that success while we were together, we appreciated that's just the way it was.

Eugene, your post-Vaselines band Captain America toured with Nirvana just as they were breaking big in 1991. What was it like to witness the maelstrom firsthand?

E: Nevermind had just been released. While we were on tour they performed Smells Like Teen Spirit on Top of the Pops and suddenly they were the biggest band in the world. It was pretty exciting. There was always someone wanting to interview them or take pictures of them, although I never really got a chance to develop a close friendship with Kurt for that reason.

What do you think Kurt took from your songs?

E: I think he liked the childlike simplicity of them. They weren't trying to get a big message across, they were just simple, funny tunes that were maybe an antidote to the heavy, visceral rock stuff he was performing.

F: My kids have just got into Nirvana and my eldest boy – he's nine – turned to me recently and said: "Mum, we prefer Nirvana's version of Molly's Lips to yours"!

Frances, is it true that Frances Cobain is named after you?

F: I've heard that, although I've also heard she's named after Frances Farmer the actress. But if it's true it's a huge compliment. I would love to meet her.

What have you resolved to do differently or better with the Vaselines this time around?

F: I've resolved to practise more. We never used to rehearse, that was our downfall. I only learned to play those bloomin' songs properly recently. Every Vaselines concert in the past was always a bit of a disaster because I could never remember the whole songs, although we were usually too howling drunk to care. There are still mistakes but we can cover them up a bit more cleverly now.

E: We haven't really thought about how we can do it better than the last time, we're just determined to enjoy it and have fun while it's going on.